A fluid container displacement pump, in one embodiment, includes a pump housing defining a pump chamber for holding a fluid to be dispensed to a patient, at least one actuating member movable relative to the pump housing and extending through at least one opening defined in the pump housing, and a cover member disposed in the pump chamber opposite the actuating member. The fluid container displacement pump, in another embodiment, includes a pump housing defining a pump chamber for holding a fluid to be dispensed to a patient, at least one actuating member movable relative to the pump housing and extending through at least one opening defined in the pump housing, a fluid reservoir defining a reservoir chamber in fluid communication with the pump housing, and a control valve controlling fluid flow between the reservoir chamber and the pump chamber.